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arXiv:1811.10552 · New Journal of Physics

Semi-device-independent quantum money

Karol Horodecki, Maciej Stankiewicz

Published Jan 7, 2020• 16 citations
arXivHTMLPDF

Abstract

Abstract The seminal idea of quantum money, not forgeable due to laws of Quantum Mechanics, proposed by Stephen Wiesner, has laid the foundations for the Quantum Information Theory in the early ’70s. Recently, several other schemes for quantum currencies have been proposed, all, however, relying on the assumption that the quantum source device, acts according to its specification. This makes several known quantum money protocols vulnerable to the so-called hardware Trojan horse attacks. We, therefore, study the following problem: to what extent quantum money schemes can be made independent from the inner working of source and verification-devices used by the honest parties (bank and mint) in creating and processing the quantum money? Drawing inspirations from the semi-device-independent quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its unforgeability. Finally, we formulate and discuss a quantum analog of the Oresme–Copernicus–Gresham’s law of economy, that may hold in the future.

DOI
10.1088/1367-2630/ab6872

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Abstract The seminal idea of quantum money, not forgeable due to laws of Quantum Mechanics, proposed by Stephen Wiesner, has laid the foundations for the Quantum Information Theory in the early ’70s. Recently, several other schemes for quantum currencies have been proposed, all, however, relying on the assumption that the quantum source device, acts according to its specification. This makes several known quantum money protocols vulnerable to the so-called hardware Trojan horse attacks. We, therefore, study the following problem: to what extent quantum money schemes can be made independent from the inner working of source and verification-devices used by the honest parties (bank and mint) in creating and processing the quantum money? Drawing inspirations from the semi-device-independent quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its unforgeability. Finally, we formulate and discuss a quantum analog of the Oresme–Copernicus–Gresham’s law of economy, that may hold in the future.
Abstract In the 1970s, Wiesner introduced the concept of quantum money, where quantum states serve as currency, offering physical-level unforgeability through quantum mechanics. Yet, traditional proposals often unrealistically assume personal quantum computing access for each user. To address these issues, we propose a cloud-based semi-quantum money (CSQM) scheme. This approach only requires semi-honest third-party quantum clouds, while the rest of the system, including transactions and banks, remains fully classical. We also estimate the computational power required by the quantum cloud and provide a thorough security analysis. Our approach significantly reduces the quantum resource demands on local users and facilitates seamless integration with current classical systems.
Private quantum money allows a bank to mint quantum money states that it can later verify, but that no one else can forge. In classically verifiable quantum money -- introduced by Gavinsky (CCC 2012) -- the verification is done via an interactive protocol between the bank and the user, where the communication is classical, and the computational resources required of the bank are classical. In this work, we consider memoryless interactive protocols in which the minting is likewise classical, and construct a private money scheme that achieves these two notions simultaneously (i.e., classical verification and classical minting). We call such a construction a private semi-quantum money scheme, since all the requirements from the bank in terms of computation and communication are classical.
The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client, and a payment terminal and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client, and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.
Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a "classical" hardness assumption that has nothing to do with quantum money. Our scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the "black-box" version of our scheme, where the polynomials are replaced by classical oracles, is unconditionally secure. Previously, such a result had only been known relative to a quantum oracle (and even there, the proof was never published). Even in Wiesner's original setting -- quantum money that can only be verified by the bank -- we are able to use our techniques to patch a major security hole in Wiesner's scheme. We give the first private-key quantum money scheme that allows unlimited verifications and that remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank. Our money scheme is simpler than previous public-key quantum money schemes, including a knot-based scheme of Farhi et al. The verifier needs to perform only two tests, one in the standard basis and one in the Hadamard basis -- matching the original intuition for quantum money, based on the existence of complementary observables. Our security proofs use a new variant of Ambainis's quantum adversary method, and several other tools that might be of independent interest.
The concept of quantum tokens dates back alongside quantum cryptography to Stephen Wiesner's seminal work in 1983[1]. Already this initial work proposes society-relevant applications such as secure quantum banknotes, which can be exchanged between a bank and a customer. This quantum currency is based on various physical states that can be easily verified but is protected from being copied by the fundamental quantum laws. Four decades later, these ideas have flourished in the field of quantum information, and the concept of quantum banknotes has not only adopted many varying names, such as quantum money, quantum coins, quantum-digital payments, and quantum tokens, but also reached its first experimental demonstrations. In this perspective article, we discuss the current state-of-the-art of quantum tokens in the field of quantum information, as well as their future perspectives. We present a number of physical realizations of quantum tokens with integrated quantum memories and their applicability scenarios in detail. Finally, we discuss how quantum tokens fit into the information security ecosystem and consider their relationship to post-quantum cryptography.
Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key---meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a "classical" hardness assumption that has nothing to do with quantum money. Our scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the "black-box" version of our scheme, where the polynomials are replaced by classical oracles, is unconditionally secure. Previously, such a result had only been known relative to a quantum oracle (and even there, the proof was never published).